Laplace Transform Time Shift Property

[bran_1]

Homework Statement

I’m being asked to prove if and why (what instances in which) T<0 for the Laplace transform property of time shifting doesn’t hold.

Homework Equations

L{f(t-T)}=e^-aT* F(s)

The Attempt at a Solution

I know that for T<0 there are instances where the property cannot hold, but I cannot think of an example where the property would fail. (I know the “if”, but not the “why”)

 

[scottdave]

It should be $e^{-sT} F(s)$ rather than (-aT) in the exponent

 

[bran_1]

It should be $e^{-sT} F(s)$ rather than (-aT) in the exponent

Yes, typo on my part. Its supposed to be ‘s’, the frequency domain variable, and T, the time shift.

Would you happen to have any insight to the original problem?